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Choose O if the statement is ALWAYS true. Otherwise, choose X. No need for justifications. (a.) The logic expressions (p → (q→r)) and ((p ^ q) → r) are logically equivalent. (b.) Suppose the proposition p V q is true, but we do not know which of p or q is true. If pr and q→r, then regardless of which of p or q is true, then we can infer proposition r to be true. (c.) Let A be a finite set of n elements. Then the number of subsets of A is n². (d.) If the symmetric difference of two sets is empty, then those two sets are equal.

Choose O if the statement is ALWAYS true. Otherwise, choose X. No need for justifications. (a.) The logic expressions (p → (q→r)) and ((p ^ q) → r) are logically equivalent. (b.) Suppose the proposition p V q is true, but we do not know which of p or q is true. If pr and q→r, then regardless of which of p or q is true, then we can infer proposition r to be true. (c.) Let A be a finite set of n elements. Then the number of subsets of A is n². (d.) If the symmetric difference of two sets is empty, then those two sets are equal.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Choose O if the statement is ALWAYS true. Otherwise, choose X. No need for justifications. ◆ (a.) The logic expressions (p → (q→r)) and ((p ^ q) →r) are logically equivalent. ◆ (b.) Suppose the proposition p V q is true, but we do not know which of p or q is true. If p→r and q→ r, then regardless of which of p or q is true, then we can infer proposition r to be true. ♦ (c.) Let A be a finite set of n elements. Then the number of subsets of A is n². (d.) If the symmetric difference of two sets is empty, then those two sets are equal. + (e.) Consider the divides relation x Ryxy. If R is defined over the set of all integers Z, then R is a partial-order relation. ♦ (f.) Let X and Y be finite sets. If there exists a function f : X→ Y that is one-to-one, then X ≤ Y powerset P(S) is also countable. ◆ (g.) If a set S is countable, then its (h.) The infinite union of finite sets is countable. → (i.) Let F(x)= automorphism on (R+, .) - x². F is an ♦ (j.) The set of non-zero real numbers with arithmetic multiplication as an operation is a monoid, but not a group.
Transcribed Image Text:Choose O if the statement is ALWAYS true. Otherwise, choose X. No need for justifications. ◆ (a.) The logic expressions (p → (q→r)) and ((p ^ q) →r) are logically equivalent. ◆ (b.) Suppose the proposition p V q is true, but we do not know which of p or q is true. If p→r and q→ r, then regardless of which of p or q is true, then we can infer proposition r to be true. ♦ (c.) Let A be a finite set of n elements. Then the number of subsets of A is n². (d.) If the symmetric difference of two sets is empty, then those two sets are equal. + (e.) Consider the divides relation x Ryxy. If R is defined over the set of all integers Z, then R is a partial-order relation. ♦ (f.) Let X and Y be finite sets. If there exists a function f : X→ Y that is one-to-one, then X ≤ Y powerset P(S) is also countable. ◆ (g.) If a set S is countable, then its (h.) The infinite union of finite sets is countable. → (i.) Let F(x)= automorphism on (R+, .) - x². F is an ♦ (j.) The set of non-zero real numbers with arithmetic multiplication as an operation is a monoid, but not a group.
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